Biological cells consist of cytoplasm surrounded by a membrane. The cytoplasm is conducting, the membrane, which is made up of a lipid bilayer, can be considered a dielectric. The application of electric fields to biological cells causes buildup of electrical charge at the cell membrane, and consequently a change in voltage across the membrane. For eukaryotic cells the transmembrane voltage under equilibrium condition is approximately 70 mV. In order to affect membrane processes by means of external electric fields, the amplitude of these fields ("E") must be such that it generates a potential difference ("V.sub.m ") at least on the same order as the resting potential. The amplitude of the electric field is: EQU E=V.sub.m /fa (1)
where a is the radius of the cell and f is a form factor which depends on the shape of the cell. For spherical cells, f is 1.5; for cylindrical cells of length l, with hemispheres of diameter d at each end, the form factor is EQU f=l/(l-d/3) (2)
For a biological cell with an assumed radius of about 5 .mu.m and a spherical shape, the external electric field required to generate a voltage of the same amplitude as the resting potential across the membrane is on the order of 100 V/cm. Due to their smaller size, the electric field required to affect the membrane permeability of bacteria is much higher, on the order of kV/cm.
For external electric fields of a magnitude such that the change in membrane potential is on the order of the resting potential, voltage induced opening of channels in the membrane causes flux of ions through the membrane. This leads to changes in the ion concentration close to the cell membrane, and consequently causes cell stress. The stress lasts on the order of milliseconds, and generally does not cause permanent cell damage. If the strength of the electric field is increased such that the voltage across the cell membrane reaches levels on the order of one volt, the membrane permeability increases to such a level that either the cell needs from seconds to hours to recover (reversible breakdown), or cell death may occur. The mechanism of the membrane breakdown is not well understood. A common hypothesis is that pores are generated in the membrane. The pores can be of sizes which allow the exchange of macromolecules. If the transmembrane voltages are sufficiently high the pores will not close anymore. The use of the reversible breakdown effect has been reported in electroporation and in biofouling prevention. The irreversible effect has been employed in the debacterialization of water and food.
The effect of electric fields on biological cells is not simply dependent on the magnitude of the applied electric field, but also on its duration. This can be understood by considering a model for the electrical equivalent circuit of the cell, shown schematically in FIG. 1. The model shown in FIG. 1 does not take the effect of structures inside the cell into account. The cell (in suspension) is modeled by a resistance and capacitance. For a pulse duration which is long compared to the dielectric relaxation time of the suspension, the capacitive component of the suspension impedance can be neglected. For many cell suspensions and seawater (i.e., aqueous solutions with relatively high ionic strengths) the dielectric relaxation time is on the order of nanoseconds. The cell membrane can be modeled as capacitor, the cytoplasm as a resistor. The outer membrane contains channels which are affected by the applied voltage and allow flow of ions through the membrane, representing a leakage current. The voltage-gated channels can be modeled as variable, voltage-dependent resistors.
When a voltage pulse is applied to the cell, charges accumulate at the membrane and the membrane voltage is increased. The charging time constant of the cell membrane may be represented by equation (3): EQU .tau.=(.rho..sub.1 /2+.rho..sub.2)Cr (3)
with .rho..sub.1 being the resistivity of the suspending medium, e.g. water, .rho..sub.2 being the resistivity of the cytoplasm, C the capacitance per unit area, and r the cell radius (spherical cell). Using typical data for cells, the duration of the electric field pulses required to generate a potential difference of 1 V across the membrane can be calculated. The energy, W, dissipated in the suspension is given by: EQU W=E.sup.2.tau./.rho..sub.1 (4)
Electric field and energy density are plotted in FIG. 2 versus pulse duration for spherical cells of radius 5 .mu.m in a suspension with a resistivity of 50 .OMEGA.cm. The resistivity of the cytoplasm is assumed to be 100 .OMEGA.cm. The curves show a minimum at 100 nsec. This is the pulse duration where the stunning or killing of these kind of biological cells is predicted to be most effective. Experimental studies have reported which confirm the presence of such a minimum.
Modifications of cells which lead to rupture of the cell membrane can lead to cell death via necrosis, a nonphysiological type of cell destruction. It would be advantageous to be able to initiate cell death via apoptosis in a selective manner. This would allow the destruction of cells without engendering the non-specific damage to surrounding tissues due to inflammation and scarring that is normally observed with necrosis. The ability to selectively modify cells in ways that lead to apoptosis could provide a new method for the selective destruction of undesired cells/tissue (e.g., cancer cells, fat cells or cartilage cells) while minimizing side effects on surrounding tissue.